Return the most probable speed for a particle within a Maxwellian
distribution.

Parameters:

T (Quantity) – The particle temperature in either kelvin or energy per particle

particle (str, optional) – Representation of the particle species (e.g., 'p' for protons, 'D+'
for deuterium, or 'He-4+1' for singly ionized helium-4),
which defaults to electrons. If no charge state information is
provided, then the particles are assumed to be singly charged.

method (str, optional) – Method to be used for calculating the thermal speed. Options are
'most_probable' (default), 'rms', and 'mean_magnitude'.

mass (Quantity) – The particle’s mass override. Defaults to NaN and if so, doesn’t do
anything, but if set, overrides mass acquired from particle. Useful
with relative velocities of particles.

UnitConversionError – If the particle temperature is not in units of temperature or
energy per particle

ValueError – The particle temperature is invalid or particle cannot be used to
identify an isotope or particle

Warns:

RelativityWarning – If the ion sound speed exceeds 5% of the speed of light, or

~astropy.units.UnitsWarning – If units are not provided, SI units are assumed.

Notes

The particle thermal speed is given by:

\[V_{th,i} = \sqrt{\frac{2 k_B T_i}{m_i}}\]

This function yields the most probable speed within a distribution
function. However, the definition of thermal velocity varies by
the square root of two depending on whether or not this velocity
absorbs that factor in the expression for a Maxwellian
distribution. In particular, the expression given in the NRL
Plasma Formulary [1] is a square root of two smaller than the
result from this function.